Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Programare bazată pe componente - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMA1012	Optimization Models	

Semester	Hours: C+S+L+P	Category	Status	
2	2+1+0+1	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
POPOVICI Nicolae	Ph.D.	Assoc.Prof.	Algebra, Mathematical Analysis and Geometry	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The aim of this course is to present several classical and modern optimization models, from both theoretical and practical points of view.	

IV. Course contents
Special instances of linear optimization: resource allocation problems, diet problems; integer programming (Gomory method); multicriteria linear optimization with respect to domination or lexicographic ordering; transportation problems. Nonlinear optimization models; numerical methods for solving unconstrained or constrained optimization problems (gradient methods, penalty and barrier functions methods). Dynamic programming models: the Bellman&#8217;s principle of dynamic programming; applications of its continuous and discrete versions to economics and network-type problems. Optimization models via calculus of variations: the fundamental problem of the calculus of variations; the Euler equation and some of its special cases; transversality conditions; applications.	

V. Bibliography
1. ANDERSON, D.R., SWEENEY, D.J., WILLIAMS, T.A., An Introduction to Management Science. Quantitative Approaches to Decision Making, South-Western College Publishing, Cincinnati, 2000.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operaţională, EFES, Cluj-Napoca, 2006.
3. BRECKNER, W.W.: Cercetare operationala, Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1981.
4. CHIANG, A.C.: Elements of Dynamic Optimization. McGraw-Hill, New York, 1992.
5. DACOROGNA, B.: Introduction au calcul des variations. Presses Polytechniques et Universitaires Romandes, Laussane, 1992.
6. EHRGOT, M.: Multicriteria Optimization. Springer, Berlin Heidelberg New York, 2005.
7. HILLERMEIER, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkhauser Verlag, Basel - Boston - Berlin, 2001.
8. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
9. STEFANESCU, A., ZIDAROIU, C.: Cercetari operationale, Editura Didactica si Pedagogica, Bucuresti, 1981. 
10. VANDERBEI, R.: Linear Programming. Foundations and Extensions, Springer, New York, 2008.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. POPOVICI Nicolae, Ph.D.